Question

Carlos is 5 less than 3 times his brother's age. Carlos' age is also 11 years older than his brother's age. How old is Carlos?​

Answer 1

Systems of Equations Word Problems

To solve these questions, we can translate key words into operations.

• Older = add
• Less than = subtract

Solving the Question

We're given:

• Carlos' age is 5 less than 3 times his brother's age
• Carlos' age is 11 years higher than his brother's age

There are two variables present in this problem: Carlos' age and his brother's age.

• Let Carlos' age equal x
• Let his brother's age equal y

Translate the given information into equations:

• Carlos' age is 5 less than 3 times his brother's age
  ⇒ $3y-5=x$
• Carlos' age is 11 years higher than his brother's age
  ⇒ $y+11=x$

We can solve for y, his brothers age, using substitution:

$3y-5=y+11\\2y=16\\y=8$

Now, solve for x by substituting y in either of the equations:

$y+11=x\\8+11=x\\x=19$

Therefore, Carlos is 19 years old.

Answer

Carlos is 19 years old.